Question

The diameter of the He He atom is approximately 0.10 nm nm . Calculate the density of the He atom in g/cm 3 g/cm3 (assuming that it is a sphere).

Answer 1

Answer:

Density of the He atom = 12.69 g/cm³

Explanation:

From the information given:

Since 1 mole of an atom = 6.022x 10²³ atoms)

1 atom of He = $1 \ atom \times (\dfrac{1 \ mole}{ 6.022 \times 10^{23} \ atoms}) \times ( \dfrac{4.003 \ grams}{ 1 \ mole})$

$=6.647 \times 10^{-24} \ grams$

The volume can be determined as  folows:

since the diameter of the He atom is approximately 0.10 nm

the radius of the He = $\dfrac{0.10}{2}$ = 0.05 nm

Converting it into cm, we have:

$0.05 nm \times \dfrac{10^{-9} \ meters}{ 1 nm} \times \dfrac{ 1 cm }{10^{-2} \ meters}$

$=5 \times 10^{-9} \ cm$

Assuming that it is a sphere, the volume of a sphere is

= $\dfrac{4}{3}\pi r^3$

= $\dfrac{4}{3}\pi \times (5\times 10^{-9})^3$

= $5.236 \times 10^{-25} \ cm^3$

Finally, the density can be calcuated by using the formula :

$Density = \dfrac{mass}{volume}$

$D = \dfrac{6.647 \times 10^{-24} \ grams }{ 5.236 \times 10^{-25} \ cm^3}$

D = 12.69 g/cm³

Density of the He atom = 12.69 g/cm³

Answer 2

Answer:

12.7g/cm³

Explanation:

Density is defined as the ratio of mass per unit volume of a substance.

Density = Mass/Volume

Since the shape of the Helium atom is a sphere, we will use the formula for calculating the volume of a sphere to get the volume of helium

Volume of a sphere = 4/3πr³ where r is the radius of the sphere.

Given the diameter of the sphere = 0.10nm

radius of the sphere = 0.10/2 = 0.05nm = 5*10⁻⁹cm

Volume of the sphere = 4/3 * 3.14 * (5*10⁻⁹)³

V =  4/3 * 3.14 * 125*10⁻²⁷

V = 1,570*10⁻²⁷/3

V = 523.33*10⁻²⁷

V =  5.233*10⁻²⁵cm³

Mass of the Helium atom = 6.6464731 × 10⁻²⁴ g

Density of the Helium atom in g/cm³ = 6.6464731 × 10⁻²⁴ g/5.233*10⁻²⁵cm³

Density of the Helium atom in g/cm³ = 1.27 * 10⁻²⁴⁻⁽⁻²⁵⁾g/cm³

Density of the Helium atom in g/cm³ = 1.27 * 10⁻²⁴⁺²⁵g/cm³

Density of the Helium atom in g/cm³ = 1.27 * 10¹g/cm³

Density of the Helium atom in g/cm³ = 12.7g/cm³

Hence the density of the He atom in g/cm³ is 12.7g/cm³